I have actually two projects… an MVC project and a project used for making my own MembershipProvider.
I wish the project that hold the membershipprovider to read my web.config from the MVC project to get the connectionString.
In other words.. when i add the assembly to my project MVC it must be able to go to the web.config and get the connectionString from there.
It is completely possible to read the web.config if your code is on a separate assembly or not.
For example, Entity Framework data models are usually put a separate project so that it could be reusable and entity framework model needs a connection string from web.config unless you provide one inside the constructor.
As an instance, the below method will return connectionString named myConn:
UPDATE
I am not sure what do you want here but if you want to make the ConnectionString name changeable, do it this way:
The point here is that you can access them from a different assembly as well.